Block #2,087,064

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/25/2017, 10:26:24 AM · Difficulty 10.8740 · 4,749,336 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
d126a289735ede7f217db7aa4c4b8dd6e83778e2322597af0ad339202830bc88

Height

#2,087,064

Difficulty

10.873958

Transactions

2

Size

1018 B

Version

2

Bits

0adfbbaf

Nonce

75,235,415

Timestamp

4/25/2017, 10:26:24 AM

Confirmations

4,749,336

Merkle Root

0ac343096a08b8f893984d7f9e21731689fb4b2956a7c4e2047e4427338a4443
Transactions (2)
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.059 × 10⁹²(93-digit number)
10592327562944384557…14339021062156501441
Discovered Prime Numbers
p_k = 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
1.059 × 10⁹²(93-digit number)
10592327562944384557…14339021062156501441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.118 × 10⁹²(93-digit number)
21184655125888769114…28678042124313002881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.236 × 10⁹²(93-digit number)
42369310251777538228…57356084248626005761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.473 × 10⁹²(93-digit number)
84738620503555076457…14712168497252011521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.694 × 10⁹³(94-digit number)
16947724100711015291…29424336994504023041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.389 × 10⁹³(94-digit number)
33895448201422030582…58848673989008046081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.779 × 10⁹³(94-digit number)
67790896402844061165…17697347978016092161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.355 × 10⁹⁴(95-digit number)
13558179280568812233…35394695956032184321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.711 × 10⁹⁴(95-digit number)
27116358561137624466…70789391912064368641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.423 × 10⁹⁴(95-digit number)
54232717122275248932…41578783824128737281
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,935,463 XPM·at block #6,836,399 · updates every 60s
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